Question

Media aritmetica a 5 numere este 162. Aflati numerele, stiind ca primele trei numere sunt direct proportionale cu numerele 3, 4 si 5, iar ultimele trei numere sunt direct proportionale cu 3,4 si 5

Answer 1

ma=a+b+c+d+e/5=162 a+b+c+d+e=162*5=810 (1) a, b, c d.p cu {3,4,5} a/3=b/4=c/5=k ⇒ c=5k c,d,e,d. p cu {3,4,5} c/3=d/4=e/5=k2 ⇒ c=3k2 ⇒ 3k2=5k⇒ k2=5/3*k dar a= 3k, b=4k, c=5k , d=4*k2=4*5/3*k, e=5k2=5*5/3*k inlocuiesc in (1) 3k+4k+5k+20/3*k+25/3*k= 810 12k+45/3*k=810 amplific cu 3 36k+45k=810*3 81k=810*3 ⇒ k=30 a=3*30=90 b=4*30=120 c=5*30=150 d=20*30/3=200 e= 25*30/3=250

Answer 2

a+b+c+d+e =162×5 =810
a/3 = b/4 = c/5  = k     a=3k   b=4k    c=5k
c/3 = d/4= e/5 = m      c=3m     3m=5k     m=5k/3
d=4m=4×5k/3=20k/3
e=5m=5×5k/3=25k/3
a+b+c+d+e=162×5=810
3k+4k+5k+20k/3+25k/3=810
12k+45k/3=810
36k+45k=2430
81k=2430
k=30
a=3k=3×30=90
b=4k=4×30=120
c =5k=5×30=150
d = 20k/3=20×30/3=200 
e = 25k/3=25×30/3=250